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A class of bounded starlike functions

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  • Herb Silverman

Abstract

We consider functions f ( z ) = z + … that are analytic in the unit disk and satisfy there the inequality Re ( f ′ ( z ) + z f ″ ( z ) ) > α , α < 1 . We find extreme points and then determine sharp lower bounds on Re f ′ ( z ) and Re ( f ( z ) / z ) . Sharp results for the sequence of partial sums are also found.

Suggested Citation

  • Herb Silverman, 1994. "A class of bounded starlike functions," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 17, pages 1-4, January.
    • Handle: RePEc:hin:jijmms:141459
    DOI: 10.1155/S0161171294000360
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    Cited by:

    1. Daniel Breaz & Abdullah Durmuş & Sibel Yalçın & Luminita-Ioana Cotirla & Hasan Bayram, 2023. "Certain Properties of Harmonic Functions Defined by a Second-Order Differential Inequality," Mathematics, MDPI, vol. 11(19), pages 1-14, September.

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